Physical topology design for survivable routing of logical rings in WDM-based networks

In a WDM-based network, a single physical link failure may correspond to multiple logical link failures. As a result, 2-connected logical topologies, such as rings routed on a WDM physical topology, may become disconnected after a single physical link failure. We consider the design of physical topologies that ensure logical rings can be embedded in a survivable manner. First, we develop necessary conditions on the physical topology to be able to embed all logical rings in a survivable manner. We then use these conditions to provide lower bounds on the number of physical links that an TV-node physical topology must have in order to support all logical rings for even sizes K. For example, we show that when K ≥ 4 the physical topology must have at least 4N/3 links, and that when K ≥ 6 the physical topology must have at least 3N/2 links, and when K ≥ 8 the physical topology must have at least 1.6N links. Furthermore, we show that for K ≥ N - 2 the physical topology must have at least 2N - 4 links. Finally, we design a physical topology that meets the above bound for K = N - 2. We then modify this physical topology to embed rings of size K = N - 1 and K = N.